Problem 1
A random sample has been taken from a normal distribution.
Related (computed) output from a software package follows:
Variable N Mean SE Mean StDev Variance Sum
x 10 ? 0.507 1.605 ? 251.848
Here N is the sample size, Mean is the sample average, SE mean is the standard error of the sample
mean, and Sum is the sum of the sample values.
1.1 Fill in the missing quantities.
1.2 Find a 95% CI on the population mean.
Problem 2
A healthcare provider monitors the number of CAT scans performed each month in each of its clinics. The most recent monthly data set for a particular clinic follows below. The reported variable values show the monthly number of CAT scans per thousand members of the health plan:
2.31, 2.09, 2.36, 1.95, 1.98, 2.25, 2.16, 2.07, 1.88, 1.94, 1.97, 2.02.
2.1 Find a 95% two-sided CI on the mean number of CAT scans performed monthly at this clinic.
a) 95% CI = (sqrt((n-1)s^2 / X^2a) , sqrt((n-1)s^2 / X^21-a) )
= (sqrt (110.15637^2/21.92), sqrt (110.15637^2/3.816))
= (0.11077, 0.26549)
2.2 Historically, the mean number of scans performed by all clinics in the system has been 1.95. Is there any evidence that this particular clinic performs more CAT scans on average than the overall system average?
Problem 3
A corporation conducts a statistical survey. Suppose that of 1000 customers surveyed, 850 are satisfied with the corporation’s products and services. Denote the population proportion of satisfied customers by p.
3.1 Test the hypothesis H0: p = 0.9 against H1: p ≠ 0.9 at α = 0.05.
3.2 Find the P-value.
3.3 Explain how the question posed by the hypothesis test could be answered by constructing a 95% two-sided CI for p.
Sample Solution
